Other useful tidbits from this section-- well worth reading in full at the url above:

"There is significant upwash ahead of the wing and even more downwash behind the wing."

"There is downward momentum in any air column behind the wing. There is zero momentum in any air column ahead of the wing, outboard of the trailing vortices, or aft of the starting vortex."

"Induced drag arises when you have low speed and/or short span, because you are visiting a small amount of air and yanking it down violently, producing strong wake vortices. In contrast there is very little induced drag when you have high speed and/or long span, because you are visiting a large amount of air, pulling it down gently, producing weak wake vortices."

"We know that the airplane, in order to support its weight, has to yank down on the air. The air that has been visited by the airplane will have a descending motion relative to the rest of the air. The trailing vortices mark the boundary of this region of descending air. It doesn’t matter whether you consider the vorticity to be the cause or the effect of the descending air — you can’t have one without the other."

"Lift must equal weight times load factor, and we can’t easily change the weight, or the air density, or the wingspan. Therefore, when the airplane flies at a low airspeed, it must generate lots of circulation."

"The important point remains that there is no way to produce lift without producing wake vortices. Remember: The trailing vortices mark the boundary between the descending air behind the wing and the undisturbed air outboard of the descending region."

"Like a common smoke ring, the wake vortex does not just sit there, it moves. In this case it moves downward. A common rule of thumb says they normally descend at about 500 feet per minute, but the actual rate will depend on the wingspan and coefficient of lift of the airplane that produced the vortex."

"Here are some more benefits of understanding circulation and vortices: it explains induced drag, and explains why gliders have long skinny wings. Induced drag is commonly said to be the “cost” of producing lift. However, there is no law of physics that requires a definite cost. If you could take a very large amount of air and pull it downward very gently, you could support your weight at very little cost. The cost you absolutely must pay is the cost of making that trailing vortex. For every mile that the airplane flies, each wingtip makes another mile of vortex. The circulatory motion in that vortex involves nontrivial amounts of kinetic energy, and that’s why you have induced drag. A long skinny wing will need less circulation than a short fat wing producing the same lift. Gliders (which need to fly slowly with minimum drag) therefore have very long skinny wings (limited only by strength; it’s hard to build something long, skinny, and strong)."

"A wing is amazingly effective at producing circulation, which speeds up the air above it. Even though the air that passes above the wing has a longer path, it gets to the back earlier than the corresponding air that passes below the wing."

"It is a bit of a mystery why the air hates turning a corner at the trailing edge, and doesn’t mind so much turning a sharp corner at the leading edge — but that’s the way it is.11 This is related to the well-known fact that blowing is different from sucking. (Even though you can blow out a candle from more than a foot away, you cannot suck out a candle from more than an inch or two away.) In any case, the rule is: The air wants to flow cleanly off the trailing edge."

"Below-atmospheric pressure above the wing is much more pronounced than above-atmospheric pressure below the wing."

"For the airfoil in figure 3.6, under cruise conditions, there is almost no high pressure on the bottom of the wing; indeed there is mostly suction there. The only reason the wing can support the weight of the airplane is that there is more suction on the top of the wing."

"We know that air has mass. Moving air has momentum. If the air parcel follows a curved path, there must be a net force on it, as required by Newton’s laws."

"Bernoulli’s principle is intimately related to the idea of streamline curvature discussed in section 3.3. If the parcel experiences a side-to-side pressure gradient, the direction of motion will change. If the parcel experiences a front-to-back pressure gradient, the speed of motion will change. This is exactly what we would expect from Newton’s laws of motion."

"It must be emphasized that you do not get to choose Bernoulli’s principle “instead of” Newton’s laws or vice versa. Bernoulli’s principle is a consequence of Newton’s laws. See section 3.14 for more on this."

"Bernoulli’s principle asserts that a given parcel of air has high velocity when it has low pressure, and vice versa. This is an excellent approximation under a wide range of conditions. This can be seen as a consequence of Newton’s laws."

"Do we get a little bit of lift because of Bernoulli, and a little bit more because of Newton? No, the laws of physics are not cumulative in this way."

"There is only one lift-producing process. Each of the explanations itemized above concentrates on a different aspect of this one process. The wing produces circulation in proportion to its angle of attack (and its airspeed). This circulation means the air above the wing is moving faster. This in turn produces low pressure in accordance with Bernoulli’s principle. The low pressure pulls up on the wing and pulls down on the air in accordance with all of Newton’s laws."

"The wing used on the Wright brothers’ first airplane is shown in figure 3.15. It is thin, highly cambered, and quite concave on the bottom. There is no significant difference between the top surface and the bottom surface — same length, same curvature. Still, the wing produces lift, using the same lift-producing principle as any other airfoil. This should further dispel the notion that wings produce lift because of a difference in length between the upper and lower surfaces.

Similar remarks apply to the sail of a sailboat. It is a very thin wing, oriented more-or-less vertically, producing sideways lift.

Even a thin flat object such as a barn door will produce lift, if the wind strikes it at an appropriate angle of attack. The airflow pattern (somewhat idealized) for a barn door (or the wing on a dime-store balsa glider) is shown in figure 3.16. Once again, the lift-producing mechanism is the same."

"Beware that people sometimes claim that Bernoulli’s principle only applies to “incompressible” fluids, but this claim is nonsense. There are no incompressible fluids. Air is highly compressible. The density ρ changes when the pressure P changes. The temperature changes too. All these changes are quite significant. Equations such as equation 3.5 already account for this correctly to first order; if they did not, the equations would give spectacularly wrong answers. The underlying idea is that since all these contributions are proportional to one another (to first order), you don’t need a temperature-dependent term and a density-dependent term and a pressure-dependent term; you can lump all the dependencies into a single term, which shows up as the pressure-dependent term in equation 3.5. For details on this, see section 3.4.3."

"Don’t let anybody tell you that Bernoulli’s principle can’t cope with compressibility. Even the elementary version (equation 3.4) accounts for compressibility to first order."

which all boilsdown to a simple fact:
lift occurs whenever a pressure difference occurs
Just - that -simple
be it a leaf floating in a updraft
or some carefully dsigned super duper high lift(?) foil
The lift is just a reflection of the pressure difference
The downwash- just a waste product

Steve,
The discussion in the following link is worth reading. You don't need to waste time reading the links in the first post. Make sure to read the link Norm put in post #15 and note Mark Drela's post #29.

I think it can be instructive to look at two scenarios representing opposite ends of the spectrum in terms of momentum transferred to the air by a wing.

In Scenario I, a lifting wing follows a straight path through an enormous volume of air that is unbounded on all sides. The wing exerts a force on the air that is equal and opposite the force exerted by the air on the wing (Newtonís Third Law). Because there are no solid boundaries (apart from the wing) to exert a force on the air, the force the wing exerts on the air is unbalanced. According to Newtonís Second Law, the air will experience a rate of change of momentum that is equal and opposite the force it exerts on the wing.

In Scenario II, a lifting wing follows a straight path above an enormous flat plate at an altitude much smaller than its wingspan. In this case, there are two (and only two) objects that can exert a force on the air: the wing and the plate. As in Scenario I, the wing exerts a force on the air that is equal and opposite the force exerted by the air on the wing. Unlike Scenario I, there is an additional solid boundary (the plate) that can exert a force on the air. In this scenario, the net force acting on the air is the vector sum of the force exerted by the wing on the air and the force exerted by the plate on the air. If the plate exerts no force on the air then the airís rate of momentum change is the same as in Scenario I. If the plate exerts an upward force on the air that is equal in magnitude to the downward force exerted by the wing on the air, then the airís rate of momentum change is zero. Although it involves some Physics and Calculus, you can show that in this secanrio, the net upward force associated with the pressure footprint on the plate is equal to the downward force exerted by the wing on the air. Even if you arenít inclined to believe the opposing forces exerted by the wing and plate are equal in magnitude, I think itís intuitively clear that the plate will at least exert SOME vertical force on the air (the video of the helicopter hovering over a scale certainly suggests this). Any force exerted by the plate on the air will mean there is no longer equality between upward force on the wing and the airís rate of downward momentum change.

So is it correct to say that a wing generates lift by imparting downward momentum to the air? Under a very special set of circumstances, that is 100% correct. However, once you introduce a large surface (like the ground), the situation becomes more complicated. In the limiting case of ground effect (altitude << span), a lifting wing imparts no net vertical momentum to the air. A more accurate statement is the wing imparts downward momentum to the air at a rate that depends on how the volume of air it is moving through is bounded.

This discussion does not identify a specific mechanism responsible for a wingís generation of lift. It simply suggests that to identify momentum transfer as the unique mechanism underlying a wingís generation of lift does not accurately capture the balance of all the forces at play.